Issue with certain mesh vertecies stretching away from bone physics chain
It looks like you are getting some of the deformation applied twice. 
In this case it appears to be a mix between parenting and multiple armatures.

The first thing to do is to check the "Multi Modifier" checkbox on any armature modifiers after the first.

If this doesn't work, you need to use the vertex group field on the armature modifier to make sure each vertex is only influenced by a single armature modifier.